基于快慢系统的生态传染病模型的分析

Analyzation on the Stability of the Eco-Epidemiological Model with the Fast and Slow Time Scales

建立了食饵迁移捕食者染病的生态传染病模型.考虑了两个时间尺度,建立了食饵迁移捕食者染病的快系统和种群间相互作用的慢系统,并利用快系统的平衡降低了模型的维数.通过分析Jacobian矩阵,得出了系统正平衡点的局部渐近稳定性;并通过排除周期轨的存在,进一步得出了正平衡点的全局渐近稳定性.

The eco-epidemiological model with the disease in the predators and the migration of prey was formulated.By considering two time scales,two systems were established,one is of fast time scale considering prey migration and infected predators;the other is of slow one considering the interactions between populations.The system dimension was reduced with the fast time scale.By analyzing the Jacobian matrix,the positive equilibrias＇ local asymptotical stability was obtained.Furthermore,the global asymptotical stability was obtained by excluding the existence of periodic orbit.